Solve Relativity Question: Find Distance Between Events A & B

[fzksfun]

Homework Statement

In reference frame S two events occur at the same point; event A occurs 1.90 seconds before
event B. In another frame, S′, event A occurs 2.45 seconds before event B. How far apart
are events A and B in frame S′?

Homework Equations

x'=gamma (x-vt)
t' = [t - vx/c^2] gamma

The Attempt at a Solution

I used the aforementioned mentioned Lorentz transformations. I know both T and t'. I'm trying to find x'. So I solved for x in both equations and tried to calculate x' but could not do so. Am I approaching the question correctly?

 

[CompuChip]

You can do that, but you don't want to solve for x. In the frame S, to which the coordinate x belongs, the events are at the same point, so you can take x to be zero. You know then x, t, t' and you want to find x'. You have two equations: one that will give you v, and the other can be used to then find x'.

I don't know if you have learned this already, but it may also be useful that in (special relativistically) equivalent frames such as S and S', the quantity
\Delta s^2 = - c^2 \Delta t^2 + d^2
where d^2 = \Delta x^2 + \Delta y^2 + \Delta z^2 is the "ordinary" spatial distance given by Pythagoras' law, is a constant. So you could, for example, calculate \Delta s^2 in S first and then find \Delta x in S' from that.

If you have no idea what I just said in the second paragraph, please forget it and stick to the first one, that works as well

 

[fzksfun]

Thank you so much! I can't believe I didn't realize that x = 0!